PSI - Issue 83

Mohamed Berjal et al. / Procedia Structural Integrity 83 (2026) 295–304

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Fig. 5. Variation of the nonlinear frequency ratio ௡∗ ௟ / ௟ ∗ with the maximum nondimensional displacement ௠∗ ௔௫ under different rotational stiffness conditions. Figure 5 shows that the nonlinear frequency ratio increases with vibration amplitude, indicating a hardening behavior due to geometric nonlinearity.

d 2 W(x * )/dx *2

______ Nonlinear Curvature _ _ _ _ Linear Curvature Fig. 6. Linear and nonlinear curvature distributions for ௠∗ ௔௫ = 1.5 with ఏଵ ൌλ and varying right-end rotational stiffness ఏଶ . For ௠∗ ௔௫ = 1.5, the curvature distributions are presented with a clamped left end ఏଵ ൌλ and varying right-end stiffness ఏଶ . The nonlinear solution remains smooth, while the linear model exhibits discontinuities at cable locations. The discrepancy increases with ఏଶ , especially near the attachment points, highlighting the growing influence of geometric nonlinearity under asymmetric boundary conditions. This behavior results from the uneven deformation induced by the clamped end, which enhances axial stretching and amplifies nonlinear curvature effects. This highlights the necessity of nonlinear modeling for accurate prediction. These results highlight that an appropriate selection of elastic support stiffness can be used as an effective optimization parameter. Higher rotational stiffness reduces nonlinear frequency shifts and mitigates curvature localization, thereby improving structural performance and vibration control.